class Solution {
public:
    int minInsertions(string s) {
        int n=s.size();
        vector<vector<int>> dp(n,vector<int>(n));
        for(int i=n-1;i>=0;i--)
        {
            for(int j=i+1;j<n;j++)
            {
                if(s[i]==s[j]) dp[i][j]=dp[i+1][j-1];
                else dp[i][j]=min(dp[i+1][j],dp[i][j-1])+1;
            }
        }
        return dp[0][n-1];
    }
};
